1. **State the problem:** We need to find the length of side AC (labeled as $b$) in a right triangle with side BC = 5.0 cm and angle at vertex B = 27°. 2. **Identify the knowns and unknowns:** - Side BC (adjacent to angle B) = 5.0 cm - Angle at B = 27° - Side AC (opposite to angle B) = $b$ (unknown) 3. **Formula used:** In a right triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side: $$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$$ 4. **Apply the formula:** $$\tan(27^\circ) = \frac{b}{5.0}$$ 5. **Solve for $b$:** $$b = 5.0 \times \tan(27^\circ)$$ 6. **Calculate the value:** Using a calculator, $$\tan(27^\circ) \approx 0.5095$$ So, $$b = 5.0 \times 0.5095 = 2.5475$$ 7. **Round to the nearest tenth of a centime:** Since 1 cm = 100 centimes, convert $b$ to centimes: $$2.5475 \text{ cm} = 254.75 \text{ centimes}$$ Rounding to the nearest tenth of a centime: $$254.8 \text{ centimes}$$ **Final answer:** The length of side AC is approximately **254.8 centimes**.